scholarly journals Numerical Analysis of Constrained, Time-Optimal Satellite Reorientation

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Robert G. Melton
Keyword(s):  
Numerical Analysis ◽  
High Intensity ◽  
Numerical Solutions ◽  
Pseudospectral Method ◽  
Optimal Solutions ◽  
Path Constraints ◽  
Time Optimal ◽  
Stage Process ◽  
Legendre Pseudospectral Method ◽  
Method Show

Previous work on time-optimal satellite slewing maneuvers, with one satellite axis (sensor axis) required to obey multiple path constraints (exclusion from keep-out cones centered on high-intensity astronomical sources) reveals complex motions with no part of the trajectory touching the constraint boundaries (boundary points) or lying along a finite arc of the constraint boundary (boundary arcs). This paper examines four cases in which the sensor axis is either forced to follow a boundary arc, or has initial and final directions that lie on the constraint boundary. Numerical solutions, generated via a Legendre pseudospectral method, show that the forced boundary arcs are suboptimal. Precession created by the control torques, moving the sensor axis away from the constraint boundary, results in faster slewing maneuvers. A two-stage process is proposed for generating optimal solutions in less time, an important consideration for eventual onboard implementation.

scholarly journals A Numerical Computation Approach for the Optimal Control of ASP Flooding Based on Adaptive Strategies

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Shurong Li ◽  
Yulei Ge
Keyword(s):  
Optimal Control ◽  
Numerical Computation ◽  
Numerical Solutions ◽  
Pseudospectral Method ◽  
Adaptive Strategies ◽  
Terminal Condition ◽  
Constraint Aggregation ◽  
Asp Flooding ◽  
Time Optimal ◽  
Ks Function

A numerical computation approach based on constraint aggregation and pseudospectral method is proposed to solve the optimal control of alkali/surfactant/polymer (ASP) flooding. At first, all path constraints are aggregated into one terminal condition by applying a Kreisselmeier-Steinhauser (KS) function. After being transformed into a multistage problem by control vector parameter, a normalized time variable is introduced to convert the original problem into a fixed final time optimal control problem. Then the problem is discretized to nonlinear programming by using Legendre-Gauss pseudospectral method, whose numerical solutions can be obtained by sequential quadratic programming (SQP) method through solving the KKT optimality conditions. Additionally, two adaptive strategies are applied to improve the procedure: (1) the adaptive constraint aggregation is used to regulate the parameter ρ in KS function and (2) the adaptive Legendre-Gauss (LG) method is used to adjust the number of subinterval divisions and LG points. Finally, the optimal control of ASP flooding is solved by the proposed method. Simulation results show the feasibility and effectiveness of the proposed method.

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

Chebyshev multidomain pseudospectral method to solve cardiac wave equations with rotational anisotropy

2018 ◽  
Vol 09 (04) ◽  
pp. 1850025 ◽  
Author(s):  
Jairo Rodríguez-Padilla ◽  
Daniel Olmos-Liceaga
Keyword(s):  
Wave Propagation ◽  
Numerical Methods ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Pseudospectral Method ◽  
Finite Difference Schemes ◽  
Cardiac Models ◽  
Computational Resources ◽  
Realistic Geometries

The implementation of numerical methods to solve and study equations for cardiac wave propagation in realistic geometries is very costly, in terms of computational resources. The aim of this work is to show the improvement that can be obtained with Chebyshev polynomials-based methods over the classical finite difference schemes to obtain numerical solutions of cardiac models. To this end, we present a Chebyshev multidomain (CMD) Pseudospectral method to solve a simple two variable cardiac models on three-dimensional anisotropic media and we show the usefulness of the method over the traditional finite differences scheme widely used in the literature.

Time-optimal Energy Management of the Formula 1 Power Unit with Active Battery Path Constraints

2021 ◽  
Author(s):  
Pol Duhr ◽  
Maximilian Schaller ◽  
Luca Arzilli ◽  
Alberto Cerofolini ◽  
Christopher H. Onder
Keyword(s):  
Power Unit ◽  
Energy Management ◽  
Optimal Energy ◽  
Path Constraints ◽  
Time Optimal ◽  
Optimal Energy Management

Multiobjective gearshift optimization with Legendre pseudospectral method for seamless two-speed transmission

2020 ◽  
Vol 145 ◽  
pp. 103682
Author(s):  
Yanwei Liu ◽  
Ziyue Lin ◽  
Kegang Zhao ◽  
Jie Ye ◽  
Xiangdong Huang
Keyword(s):  
Pseudospectral Method ◽  
Legendre Pseudospectral Method

Peridynamics for Numerical Analysis

2021 ◽  
pp. 31-52
Author(s):  
Erdogan Madenci ◽  
Atila Barut
Keyword(s):  
Data Analysis ◽  
Numerical Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Value Problems ◽  
Entire Range ◽  
Numerical Solutions ◽  
Jump Discontinuity ◽  
Differentiation Process ◽  
Computational Mathematics

Discrete data analysis and numerical solutions to boundary and initial value problems of ordinary/partial differential equations are essential in almost every branch of science. Although the differentiation process is usually more direct than integration in analytical mathematics, the reverse is true in computational mathematics, especially in the presence of a jump discontinuity or a singularity. Integration is a nonlocal process because it depends on the entire range of integration. However, differentiation is a local process.

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